New Zealand prime minister Jacinda Ardern has revealed the country will be issuing gifts in honour of the royal baby.
Meghan's pregnancy was announced as she and Harry embarked on a tour of Australia and New Zealand last year.
And Ms Ardern said: “A donation will be made to a group called Little Sprouts who prepares baby boxes for families in need on the birth of their babies.
“And also, we'll be purchasing 10 trees through the Trees That Count programme, native trees to acknowledge the birth of their baby.
"So, they'll be planted here in New Zealand as well. So, I hope New Zealanders think those are nice gifts on their behalf."
Last year Ms Ardern became only the second elected leader in modern history to give birth while in office.
Australia prime minister Scott Morrison also sent his "huge congratulations" to the couple.
Mr Morrison, who climbed the Sydney Harbour Bridge with Harry, said it was "great that the wonderful day has come and everybody is well".
But with the Queen's role as Australia's head of state a continual topic of debate Down Under, the arrival of the seventh in line to the throne was an opportunity for critics to voice their dissatisfaction.
The Australian Republic Movement said it "warmly congratulates Harry and Meghan on the birth of their son, and all Australians who welcomed a child into the world today".
But it added in its statement: "Baby Sussex is the seventh in line for the British throne, behind Prince Harry, Prince Louis, Princess Charlotte, Prince George, Prince William and Prince Charles – making him unlikely to ever rule over Australians.
"We look forward to when our head of state is chosen by Australians, and on merit, instead of birth right.
"An Australian republic will mean that each child born today can grow up aspiring to the top job - regardless of their family, social status or wealth."
Additional reporting by Press Association
